Weight | 0-10 | 10-15 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-60 |

No, of person | 4 | 8 | 30 | 15 | 13 | 6 | 4 | 4 | 1 |

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Since the classes are unequal so adjustment is to be made before calculating.

Weight |
No. of Person (f) |
c.f. |

0-5 | 2 | 2 |

5-10 | 2 | 4 |

10-15 | 8 | 12 |

15-20 | 15 | 27 |

20-25 | 15 | 42 |

25-30 | 15 | 57 |

30-35 | 13 | 70 |

35-40 | 6 | 76 |

40-45 | 4 | 80 |

45-50 | 4 | 84 |

50-55 | 0.5 | 84.5 |

55-60 | 0.5 | 85 |

N = 85 |

Now,

For Q1:

Q_{1} = \(\left ( \frac{N}{4} \right )^{th} \enspace item\)

= \(\left ( \frac{85}{4} \right )^{th} \enspace item\) = 21.25^{th} item

In c.f column, the value just greater than 25.25 is 27. so, class is 15 – 20

Then,

Q_{1} = \(L + \frac{\frac{N}{4} – c.f.}{f} \times h\)

= \(15 + \frac{21.25 – 12}{15} \times 5\)

= 18.08

For D_{7}:

D_{7} = \(\left ( 7 \times \frac{N}{10} \right )^{th} \enspace item\)

= \(\left ( 7 \times \frac{85}{10} \right )^{th} \enspace item\) = 59.5^{th} item

In c.f column, the value just greater than 59.5 is 70. so, class is 30-35

Then,

D_{7} = \(L + \frac{\frac{7N}{10} – c.f.}{f} \times h\)

= \(30 + \frac{59.5 – 57}{13} \times 5\)

= 30.96

For P_{58}:

P_{58} = \(\left (\frac{58 N}{100} \right )^{th} \enspace item\)

= \(\left ( 7 \times \frac{58 \times 85}{100} \right )^{th} \enspace item\) = 49.3^{th} item

In c.f column, the value just greater than 49.3 is 57. so, class is 25-30

Then,

P_{58} = \(L + \frac{\frac{58N}{100} – c.f.}{f} \times h\)

= \(25 + \frac{49.3 – 43}{15} \times 5\)

= 26.43

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